In GC analysis, even if analysis is performed with the same device and under the same conditions, there is sometimes deviation in the retention times of the same component due to various factors such as fluctuations in the carrier gas flow rate over time and column deterioration. Therefore, in order to compare a plurality of chromatograms, an operation is required to correct the time axis so that the retention times of the same component are aligned roughly uniformly prior to this comparison. Although the correction of the time axis is easy if the deviation in the retention times is completely linear, deviations in retention times more often than not have nonlinearity. As one means for correcting the time axis to accommodate such nonlinear deviations in retention times, algorithms based on dynamic programming (abbreviated below as “DP”) have been proposed conventionally (see Non-Patent Document 1 and Patent Document 1).
A DP algorithm that is typically used conventionally is a technique for coordinating a reference signal (reference chromatogram signal) serving as a standard and a target signal (target chromatogram signal) for which the time axis has been distorted nonlinearly, using the degree of distortion in time and the degree of matching of the intensities at corresponding points as a cost function, and finding a correspondence relationship between the reference signal and the target signal in which the calculated cost is minimized. If such a correspondence relationship can be found, it is possible to correct deviations in retention times by nonlinearly expanding and contracting the time axis of the target signal using the correspondence relationship.
Here, for the purpose of the explanation, the reference signal will be defined as A, and a sample point at each time of the reference signal A will be expressed as A(n) (where n is a positive integer). Similarly, the target signal will be defined as B, and a sample point at each time of the target signal B will be expressed as B(n). A method for searching for the optimal (most favorably matching) correspondence relationship in typical DP is as follows (see FIG. 8).
[1] Taking into consideration the range of commonsense time fluctuations (taking into consideration the maximum values of various fluctuations), the sample point of the target signal B corresponding to the sample point A(1) of the reference signal A may correspond to “no corresponding point” or to target signal B(1) to B(3), for example.
[2] Depending on where in the aforementioned range the sample point of the target signal B corresponding to the sample point A(1) of the reference signal A lies, the group of sample points of the target signal B to which the next sample point A(2) of the reference signal A may correspond will respectively differ. For example, if the sample point of the target signal B corresponding to the sample point A(1) of the reference signal A is B(1), the group of sample points of the target signal B to which the next sample point A(2) may correspond becomes “no corresponding point” or target signal B(2) to B(4), and if the sample point of the target signal B corresponding to the sample point A(1) of the reference signal A is B(2), the group of sample points of the target signal B to which the next sample point A(2) may correspond becomes “no corresponding point” or target signal B(3) to B(5).
Accordingly, as shown in FIG. 8, the potentially corresponding sample points increase like a tree diagram as n of the sample point A(n) increases—that is, as time passes.
Assuming from a commonsense standpoint that there are m potentially corresponding candidates for each sample point when searching for an optimal correspondence relationship as described above (m=4 in the case of the example shown in FIG. 8), if the chromatogram consists of data for n sample points in total, the number of paths (that is, candidates for a correspondence relationship over the entire chromatogram) derived is approximately m to the nth power. Accordingly, the order of the number of candidates for a correspondence relationship between the reference signal A and the target signal B is O (mn), and it is necessary to calculate the cost of each candidate and select the candidate with the lowest cost.
However, there are limitations to the amount of calculations that can be processed due to limitations in the performance of the computer used for calculation or the calculation time, so it is not realistic to perform cost calculations by searching for all of an enormous number of candidates as described above. Therefore, a technique is ordinarily used in which the final number of candidates is limited to x candidates by leaving behind only the top x candidates at each stage of the search and deleting all other data. Such a technique is typically called beam limiting with a beam width x. Although the required processing time is shortened as the beam width x is narrowed, if the beam width x is made unnecessarily narrow, there is an increased probability of falling into a localized solution in which the matching in only the first half of the search is satisfactory and the matching in the second half is poor, and the method is typically weak with regard to noise and the like. Conversely, in order to provide resistance (robustness) against such noise, it is necessary to allow an enormous amount of time for calculation processing.
That is, when applying a typical DP algorithm such as that described in Non-Patent Document 1 or Patent Document 1 to the correction of the time axis of a chromatogram, it is not possible to appropriately match the target signal to the reference signal in a realistic amount of calculation processing time under unfavorable conditions such as a large number of peaks appearing in the chromatogram due to a large number of contained components, a large number of peaks due to poor S/N of the obtained signal, or extremely large fluctuations over time, which leads to the risk that the time axis may be corrected inaccurately. In particular, the probability that it will not be possible to accurately correct the time axis increases substantially in cases in which there are large fluctuations over time due to column replacement in GC analysis or cases in which a sample containing an enormous number of components such as gasoline or a perfume is analyzed.